Abstract

We describe broadband coherent transmission studies of two-dimensional photonic crystals consisting of a hexagonal array of air holes in a dielectric slab in a planar waveguide. By filling several of the air holes in the photonic crystal slab, we observe the signature of a defect mode within the stop band, in both the amplitude and phase spectra. The experimental results are in reasonable agreement with theoretical calculations using the transfer matrix method.

Figures (3)

Top, 2D band structure (TM polarization)
of the photonic crystal used in these measurements. This band structure is computed assuming an infinite slab thickness.20 The shaded boxes indicate the full gap (darker) and the pseudogap (lighter), and the dashed bands are antisymmetric and therefore do not couple to the incident beam. Bottom, schematic of the experimental setup. The photonic crystal is placed within the copper waveguide for transmission measurements.

Typical time-domain THz waveform measured in transmission through the photonic crystal slab. Insets, waveform when the waveguide contains air (top) and a solid silicon slab (bottom). In all three cases the distance between the two copper plates is 300µm, the thickness of the photonic crystal slab.

(a) Experimental transmission spectrum for the photonic crystal, relative to a solid silicon slab of equal thickness. Filled squares, perfect lattice; open circles, the same lattice but with three holes filled in the pattern shown in the inset. A defect mode appears at ∼0.28THz. (b) Solid curve, TMM calculation for a perfect photonic crystal; dotted curve, lattice with a three-point defect. The material filling the holes is assumed to be a uniform dielectric with ∊=5.0. (c) Difference in the spectral phases of the two measured waveforms that gave the spectra in (a). The signature of the defect mode is evident at 0.28 THz. The shaded area denotes the region of the full photonic bandgap, where the transmitted intensity is not large enough for accurate determination of the phase.